Problem 12 - Prealgebra

Question

Write each number as a fraction or a mixed number. Do not reduce your answers. $$60.06$$

Step-by-Step Solution

Answer

The number is written as the mixed number \( 60 \frac{6}{100} \).

Step 1: Identify the Whole Number and the Decimal Part

Analyze the given number, which is 60.06. Identify the whole number, which is 60, and the decimal part, which is 0.06.

Step 2: Convert the Whole Number to a Fraction

The whole number 60 can be represented as a fraction with a denominator of 1. Therefore, write 60 as \( \frac{60}{1} \).

Step 3: Convert the Decimal to a Fraction

The decimal 0.06 can be rewritten as a fraction. Notice that 0.06 means 6 hundredths, which is \( \frac{6}{100} \).

Step 4: Combine the Whole Number and the Fraction

Combine the whole number fraction \( \frac{60}{1} \) with the fraction \( \frac{6}{100} \). This results in the mixed number \( 60 \frac{6}{100} \).

Key Concepts

Decimal to Fraction Conversion

Converting decimals to fractions might seem confusing at first, but it's a straightforward process once you get the hang of it! When you deal with a decimal, focus on the digits after the decimal point. For instance, consider the decimal 0.06. You need to understand that 0.06 represents six hundredths.

• The number of digits after the decimal translates into your denominator's zeros. Here, there are two digits, so our base for hundreds is 100.
• Thus, 0.06 equals \( \frac{6}{100} \).

A helpful tip to remember is that if a decimal ends in the tenths, it's over 10. If it ends in hundredths, it's over 100, and so forth. The key is accurately interpreting the decimal into its fraction counterpart without altering the value.

Mixed Number Representation

A mixed number includes both a whole number and a fraction. In our exercise, we have the decimal number 60.06. It is expressed as a mixed number by separating out the whole part and the fractional part.

• First, the number 60 is a whole number and can stand by itself.
• The decimal part, 0.06, is already converted into a fraction, \( \frac{6}{100} \).

So, when combined together, 60.06 is expressed as the mixed number \( 60 \frac{6}{100} \). Working with mixed numbers requires you to systematically separate and combine the whole and fractional parts individually. This approach simplifies any complex number into manageable parts, making mathematical tasks much easier.

Whole Number as a Fraction

Understanding how to represent whole numbers as fractions is a fundamental concept in math. Any whole number can be written as a fraction by adding the denominator 1. For example, when we have the whole number 60.

• We see this number as \( \frac{60}{1} \).
• This means 60 parts of 1 whole.

Transforming a whole number into this fraction form can help simplify the process of adding, subtracting, multiplying, or dividing these numbers with other fractions. It keeps calculations consistent and introduces flexibility when combining with other fractional parts, such as our \( \frac{6}{100} \) in the exercise. Knowing how to transition between whole numbers and fractions will provide a stronger foundation when tackling more advanced math problems.